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A173850
Number of permutations of 1..n with no adjacent pair summing to n+10.
0
1, 1, 2, 6, 24, 120, 720, 5040, 40320, 362880, 3628800, 32659200, 399168000, 4470681600, 64186214400, 855496857600, 14073067008000, 216999220838400, 4018570511155200, 70276861528473600, 1445722935681024000, 28251875803447296000, 638889942904012800000
OFFSET
0,3
COMMENTS
If a(n,k) is the number of permutations of 1..n with no adjacent pair summing to n+k, then a(n,k) = a(n,k+1) for n+k even.
FORMULA
k = 10; m = max(0, floor((n-k+1)/2)); a(n,k) = Sum_{j=0..m} (-2)^j * binomial(m,j)*(n-j)!.
CROSSREFS
Sequence in context: A276844 A273697 A177281 * A154658 A179369 A267390
KEYWORD
nonn
AUTHOR
R. H. Hardin, Feb 26 2010
EXTENSIONS
Comment proved by William Keith, formula from Max Alekseyev, on the Sequence Fans Mailing List
More terms from Alois P. Heinz, Jan 09 2017
STATUS
approved